Acoustic eigenvalue estimation using the matrix pencil method and Rayleigh quotient iteration

The acoustic eigenvalues of an enclosure quantify its resonant frequencies and damping coefficients. This information can be used to determine the acoustic characteristics of a room. Various methods for estimating eigenvalues from a measured room impulse response can be found in the literature. Of these methods, the matrix pencil method is considered in this work. The matrix pencil method provides acceptable eigenvalue estimates, albeit alongside several spurious eigenvalues. In this work, the appearance of spurious eigenvalues is demonstrated by analyzing an analytic impulse response. Additionally, the use of the well-known Rayleigh quotient iteration algorithm to search for eigenvalues close to informed initial guesses and, thus, to minimize the estimation of spurious eigenvalues is presented. The approach is verified using finite element eigensolutions of a room.